Heat olive oil in a large heavy pot over high heat until hot. Pat the beef dry with paper towels, season with salt and pepper, and brown in 2–3 batches. Transfer the browned beef to a bowl and set aside.
1 tablespoon olive oil, 1 pound stewing beef, ½ teaspoon salt, ½ teaspoon black pepper
Add a little more oil if the pot is dry. Sauté onion and garlic for 2 minutes. Stir in the celery and carrots, and cook for another 2 minutes, until the onion is soft.
1 onion, 3 garlic cloves, 2 celery stalks, 3 carrots
Sprinkle flour over the vegetables and stir well. Slowly pour in the beef broth, stirring constantly to prevent lumps.
4 tablespoons all-purpose flour, 6 cups beef broth or beef stock
Add tomato paste, bay leaves, thyme, potatoes, and the browned beef. Stir to combine. Cover, reduce heat to medium-low, and simmer for about 45 minutes, or until the beef is tender.
2 tablespoons tomato paste, 2 bay leaves, 1 teaspoon dried thyme, 2 potatoes
Add peas and cook uncovered for 15–20 minutes, until the potatoes are tender and the soup has thickened. Adjust seasoning with salt and pepper.
1 cup frozen peas
Ladle the soup into bowls and garnish with fresh parsley. Serve with crusty bread for dipping.